We have presented only particular examples of super Minkowski spaces, however one can construct new examples from this list by dimensional reduction, i.e. by considering fields which are invariant under some space-time direction. For instance one can construct super extensions of the usual Minkowski space \(M^{1,3}\)  with more than 4 odd dimensions: \(M^{(1,3)|8}\)  (related to \(N=2\)  supersymmetric theories), which can be obtained by reduction of \(M^{(1,5)|8}\)  and \(M^{(1,3)|16}\)  (related to \(N=4\)  supersymmetric theories), which can be obtained by reduction of \(M^{(1,9)|16}\) . Our first example \(M^{(1,3)|4}\)  corresponds to \(N=1\)  supersymmetric theories. Similar reductions leads to various super space-times with 2 even dimensions, which are important for the theory of superstrings (see e.g. [1]}). In the following we present alternative representations of \(\mathfrak {m}^{(1,5)|8}\)  and \(\mathfrak {m}^{(1,9)|16}\)  which shows how one can produce \(N=2\)  and \(N=4\)  supersymmetry groups over \(M^{1,3}\)  with central extensions.
